1. Warmup
Let f(x) = x – 3 and g(x) = x2.
What is (f ○ g)(1)?

2. 5-3 Inverse Functions and Relations
Find the inverse of a function or a relation. Determine whether two functions or relations are inverses of each other.

3. Two functions f and g are inverses if the domain of f becomes the range of the g, and the range of f becomes the domain of g.

4. Find the inverse of each relation
2. {(-2, 9), (4, -1), (-7, 9), (7, 0)}

5. Method for finding inverses
Replace f(x) with y.
Interchange x and y.
Solve for y if possible
If there is only one y-value possible for each x-value in the inverse, you can write the inverse with function notation, and it is called f -1(x) (read this as f inverse of x)

6. Find the inverse of each function. Then graph the function.
4. 𝑔(𝑥)=4𝑥−6

7. Find the inverse of each function. Then graph the function.

8. A function and its inverse are reflections across the line y = x
When you describe a function and then describe its inverse, you can see that the steps in the function are reversed, and you have inverse operations (they undo each other)
#4 𝑔 𝑥 =4𝑥 −6
𝑔 −1 𝑥 = 𝑥+6 4

9. Find the inverse of each function
Find the inverse of each function. Then graph the function and its inverse.
23. 𝑓 𝑥 = 𝑥

10. Horizontal line test checks to see if a function has an inverse function
Use the horizontal line test to determine whether the inverse of each function is also a function.